He also wouldn't make an endorsement for who should replace Cantor, R-Va., as the No. 2 member of the House GOP.

"Members are going to make this decision," Boehner said, adding that he can "work with anyone" who might get the job — whether it's current Majority Whip Kevin McCarthy, R-Calif., Rules Chairman Pete Sessions, R-Texas, or perhaps even Idaho Republican Raúl R. Labrador.